{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T22:24:20Z","timestamp":1759962260965,"version":"3.40.3"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319684444"},{"type":"electronic","value":"9783319684451"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-68445-1_58","type":"book-chapter","created":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T00:40:36Z","timestamp":1508805636000},"page":"495-502","source":"Crossref","is-referenced-by-count":3,"title":["Hamilton-Jacobi Theory and Information Geometry"],"prefix":"10.1007","author":[{"given":"Florio M.","family":"Ciaglia","sequence":"first","affiliation":[]},{"given":"Fabio","family":"Di Cosmo","sequence":"additional","affiliation":[]},{"given":"Giuseppe","family":"Marmo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,10,24]]},"reference":[{"key":"58_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-4-431-55978-8","volume-title":"Information Geometry and its Application","author":"SI Amari","year":"2016","unstructured":"Amari, S.I.: Information Geometry and its Application. Springer, Tokyo (2016)"},{"key":"58_CR2","doi-asserted-by":"crossref","DOI":"10.1214\/lnms\/1215467056","volume-title":"Differential Geometry in Statistical Inference","author":"SI Amari","year":"1987","unstructured":"Amari, S.I., Barndorff-Nielsen, O.E., Kass, R.E., Lauritzen, S.L., Rao, C.R.: Differential Geometry in Statistical Inference. Institute of Mathematical Statistics, Hayward (1987)"},{"key":"58_CR3","volume-title":"Methods of Information Geometry","author":"SI Amari","year":"2000","unstructured":"Amari, S.I., Nagaoka, H.: Methods of Information Geometry. American Mathematical Society, Providence (2000)"},{"issue":"7","key":"58_CR4","doi-asserted-by":"crossref","first-page":"3878","DOI":"10.3390\/e16073878","volume":"16","author":"R Balian","year":"2014","unstructured":"Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878\u20133888 (2014)","journal-title":"Entropy"},{"issue":"1\u20132","key":"58_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0370-1573(86)90005-0","volume":"131","author":"R Balian","year":"1986","unstructured":"Balian, R., Alhassid, Y., Reinhardt, H.: Dissipation in many-body systems: a geometric approach based on information theory. Phys. Rep. 131(1\u20132), 1\u2013146 (1986)","journal-title":"Phys. Rep."},{"issue":"11","key":"58_CR6","doi-asserted-by":"crossref","first-page":"386","DOI":"10.3390\/e18110386","volume":"18","author":"F Barbaresco","year":"2016","unstructured":"Barbaresco, F.: Geometric theory of heat from souriau lie groups thermodynamics and koszul hessian geometry: applications in information geometry for exponential families. Entropy 18(11), 386\u2013426 (2016)","journal-title":"Entropy"},{"issue":"07","key":"58_CR7","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1142\/S0219887806001764","volume":"03","author":"JF Cari\u00f1ena","year":"2006","unstructured":"Cari\u00f1ena, J.F., Gr\u00e0cia, X., Marmo, G., Mart\u00ednez, E., Lecanda, M.C.M., Rom\u00e1n-Roy, N.: Geometric hamilton-jacobi theory. Int. J. Geom. Methods Mod. Phys. 03(07), 1417\u20131458 (2006)","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"58_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-9220-2","volume-title":"Geometry from Dynamics, Classical and Quantum","author":"JF Cari\u00f1ena","year":"2015","unstructured":"Cari\u00f1ena, J.F., Ibort, A., Marmo, G., Morandi, G.: Geometry from Dynamics, Classical and Quantum. Springer, Berlin (2015)"},{"key":"58_CR9","volume-title":"Statistical Decision Rules and Optimal Inference","author":"NN Cencov","year":"1982","unstructured":"Cencov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982)"},{"key":"58_CR10","doi-asserted-by":"crossref","unstructured":"Ciaglia, F.M., Di Cosmo, F., Felice, D., Mancini, S., Marmo, G., P\u00e9rez-Pardo, J.M.: Hamilton-jacobi approach to potential functions in information geometry. J. Mathe. Phys. 58(6) (2017)","DOI":"10.1063\/1.4984941"},{"key":"58_CR11","volume-title":"The Variational Principles of Mechanics","author":"C Lanczos","year":"1952","unstructured":"Lanczos, C.: The Variational Principles of Mechanics. University of Toronto Press, Toronto (1952)"},{"key":"58_CR12","first-page":"302","volume":"50","author":"VI Man\u2019ko","year":"2016","unstructured":"Man\u2019ko, V.I., Marmo, G., Ventriglia, F., Vitale, P.: Metric on the space of quantum states from relative entropy. Tomographic reconstruction. J. Phys. A: Math. Theor. 50, 302\u2013335 (2016)","journal-title":"J. Phys. A: Math. Theor."},{"key":"58_CR13","doi-asserted-by":"crossref","unstructured":"Marle, C.M.: From tools in symplectic and poisson geometry to J.-M. Souriau\u2019s theories of statistical mechanics and thermodynamics. Entropy 18(10) (2016)","DOI":"10.3390\/e18100370"},{"key":"58_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02832785","volume":"13","author":"G Marmo","year":"1990","unstructured":"Marmo, G., Morandi, G., Mukunda, N.: A geometrical approach to the hamilton-jacobi form of dynamics and its generalizations. La Rivista del Nuovo Cimento 13, 1\u201374 (1990)","journal-title":"La Rivista del Nuovo Cimento"},{"key":"58_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02740487","volume":"6","author":"G Marmo","year":"1983","unstructured":"Marmo, G., Mukunda, N., Samuel, J.: Dynamics and symmetry for constrained systems: a geometrical analysis. La Rivista del Nuovo Cimento 6, 1\u201362 (1983)","journal-title":"La Rivista del Nuovo Cimento"},{"key":"58_CR16","unstructured":"Marmo, G., Rubano, C.: Particle Dynamics on Fiber Bundles. Bibliopolis (1988)"},{"issue":"2","key":"58_CR17","doi-asserted-by":"crossref","first-page":"327","DOI":"10.32917\/hmj\/1206128255","volume":"23","author":"T Matumoto","year":"1993","unstructured":"Matumoto, T.: Any statistical manifold has a contrast function: on the $$ c^{3}$$ -functions taking the minimum at the diagonal of the product manifold. Hiroshima Mathe. J. 23(2), 327\u2013332 (1993)","journal-title":"Hiroshima Mathe. J."},{"key":"58_CR18","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0370-1573(90)90137-Q","volume":"188","author":"G Morandi","year":"1990","unstructured":"Morandi, G., Ferrario, C., Vecchio, G.L., Marmo, G., Rubano, C., Rubano, C.: The inverse problem in the calculus of variations and the geometry of the tangent bundle. Phys. Rept. 188, 147\u2013284 (1990)","journal-title":"Phys. Rept."},{"key":"58_CR19","volume-title":"Quantum Information Theory and Quantum Statistics","author":"D Petz","year":"2007","unstructured":"Petz, D.: Quantum Information Theory and Quantum Statistics. Springer, Heidelberg (2007)"},{"key":"58_CR20","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0024-3795(94)00211-8","volume":"244","author":"D Petz","year":"1996","unstructured":"Petz, D., Sud\u00e1r, C.: Monotone metrics on matrix spaces. Linear Algebra Appl. 244, 81\u201396 (1996)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"58_CR21","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1103\/PhysRevD.23.357","volume":"23","author":"WK Wootters","year":"1981","unstructured":"Wootters, W.K.: Statistical distance and hilbert space. Phys.Rev. D 23(2), 357\u2013362 (1981)","journal-title":"Phys .Rev. D"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-68445-1_58","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T13:05:38Z","timestamp":1693141538000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-68445-1_58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319684444","9783319684451"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-68445-1_58","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}